Question: Find the quotient when $7x^3 + 3x^2 - 5x - 8$ is divided by $x + 2.$
The long division is shown below.

\[
\begin{array}{c|cc cc}
\multicolumn{2}{r}{7x^2} & -11x & +17  \\
\cline{2-5}
x + 2 & 7x^3 & +3x^2&-5x&-8  \\
\multicolumn{2}{r}{7x^3} & +14x^2& \\ 
\cline{2-3}
\multicolumn{2}{r}{} & -11x^2& -5x\\ 
\multicolumn{2}{r}{} & -11x^2& -22x\\ 
\cline{3-4}
\multicolumn{2}{r}{} & & +17x & -8 \\ 
\multicolumn{2}{r}{} & & +17x & +34 \\ 
\cline{4-5}
\multicolumn{2}{r}{} & & & -42 \\ 
\end{array}
\]Thus, the quotient is $\boxed{7x^2 - 11x + 17}.$